Tahsin Oner - Department of Mathematics, Ege University, ۳۵۱۰۰ Izmir, Turkey
Tugce Katican - Department of Mathematics, Ege University, ۳۵۱۰۰ Izmir, Turkey
Arsham Borumand Saeid - Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.

In this paper, we introduce a Sheffer stroke Hilbert algebra by giving definitions of Sheffer stroke and a Hilbert algebra. After it is shown that the axioms of Sheffer stroke Hilbert algebra are independent, it is given some properties of this algebraic structure. Then it is stated the relationship between Sheffer stroke Hilbert algebra and Hilbert algebra by defining a unary operation on Sheffer stroke Hilbert algebra. Also, it is presented deductive system and ideal of this algebraic structure. It is defined an ideal generated by a subset of a Sheffer stroke Hilbert algebra, and it is constructed a new ideal of this algebra by adding an element of this algebra to its ideal.

Hilbert algebra, Sheffer stroke, Sheffer stroke Hilbert algebra